Viscous fingering in porous media occurs when the (miscible or immiscible) displacing fluid has a lower viscosity than the displaced fluid. For example, immiscible fingering is observed in experiments where water displaces a much more viscous oil. Modelling the observed fingering patterns in immiscible viscous fingering has proven to be very challenging, which has often been identified as being due to numerical issues. However, in a recent paper (Sorbie et al. in Transp. Porous Media 133:331–359, 2020) suggested that the modelling issues are more closely related to the physics and formulation of the problem. They proposed an approach based on the fractional flow curve, $${f}_{w}^{*}$$ f w ∗ , as the principal input, and then derived relative permeabilities which give the maximum total mobility. Sorbie et al. were then able to produce complex, well-resolves immiscible finger patterns using elementary numerical methods. In this paper, this new approach to modelling immiscible viscous fingering is tested by performing direct numerical simulations of previously published experimental water/oil displacements in 2D sandstone porous media. Experiments were modelled at adverse viscosity ratios ($${\mu }_{o}/{\mu }_{w}$$ μ o / μ w ), with oil viscosities ranging from μo = 412 to 7000 cP, i.e. for a viscosity ratio range, ($${\mu }_{o}/{\mu }_{w}$$ μ o / μ w ) $$\sim$$ ∼ 400–7000. These experiments have extensive production data as well as in situ 2D immiscible fingering images, measured by X-ray scanning. In all cases, very good quantitative agreement between experiment and modelling results is found, providing a strong validation of the new modelling approach. The underlying parameters used in the modelling of these unstable immiscible floods, the $${f}_{w}^{*}$$ f w ∗ functions, show very consistent and understandable variation with the viscosity ratio, ($${\mu }_{o}/{\mu }_{w}$$ μ o / μ w ).

Polymer flooding has gained much interest within the oil industry in the past few decades as one of the most successful chemical enhanced oil recovery (CEOR) methods. The injectivity of polymer solutions in porous media is a key factor in polymer flooding projects. The main challenge that faces prediction of polymer injectivity in field applications is the inherent non-Newtonian behavior of polymer solutions. Polymer in situ rheology in porous media may exhibit complex behavior that encompasses shear thickening at high flow rates in addition to the typical shear thinning at low rates. This shear-dependent behavior is usually measured in lab core flood experiments. However, data from field applications are usually limited to the well bottom-hole pressure (BHP) as the sole source of information. In this paper, we analyze BHP data from field polymer injectivity test conducted in a Middle Eastern heterogeneous carbonate reservoir characterized by high-temperature and high-salinity (HTHS) conditions. The analysis involved incorporating available data to build a single-well model to simulate the injectivity test. Several generic sensitivities were tested to investigate the impact of stepwise variation in injection flow rate and polymer concentration. Polymer injection was reflected in a non-linear increase in pressure with injection, and longer transient behavior toward steady state. The results differ from water injection which have linear pressure response to rate variation, and quick stabilization of pressure after rate change. The best match of the polymer injection was obtained with complex rheology, that means the combined shear thickening at high rate near the well and moving through apparent Newtonian and shear thinning at low rate.

Polymer flooding is an enhanced oil recovery (EOR) process, which has received increasing interest in the industry. In this process, water-soluble polymers are used to increase injected water viscosity in order to improve mobility ratio and hence improve reservoir sweep. Polymer solutions are non-Newtonian fluids, i.e., their viscosities are shear dependent. Polymers may exhibit an increase in viscosity at high shear rates in porous media, which can cause injectivity loss. In contrast, at low shear rates they may observe viscosity loss and hence enhance the injectivity. Therefore, due to the complex non-Newtonian rheology of polymers, it is necessary to optimize the design of polymer injectivity tests in order to improve our understanding of the rheology behavior and enhance the design of polymer flood projects. This study has been addressing what information that can be gained from polymer injectivity tests, and how to design the test for maximizing information. The main source of information in the field is from the injection bottom-hole pressure (BHP). Simulation studies have analyzed the response of different non-Newtonian rheology on BHP with variations of rate and time. The results have shown that BHP from injectivity tests can be used to detect in-situ polymer rheology.

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